[tex]\bf 2\frac{1}{4}x-3\frac{1}{2}=-\cfrac{1}{16}\implies \cfrac{2\cdot 4+1}{4}x-\cfrac{3\cdot 2+1}{2}=-\cfrac{1}{16}
\\\\\\
\cfrac{9x}{4}-\cfrac{7}{2}=-\cfrac{1}{16}[/tex]
and now, we multiply both sides by 16, to get rid of the denominators, so, let's do so.
[tex]\bf 16\cdot \cfrac{9x}{4}-16\cdot \cfrac{7}{2}=16\cdot -\cfrac{1}{16}\implies 36x-56=-1
\\\\\\
36x=55\implies x=\cfrac{55}{36}[/tex]
